Remark 1 In practice, \(\mathbf {y}\)  and \(\mathbf {K}\)  are given by real-valued vectors, and \(\mathcal {M}\)  is not necessarily the same as \(\mathbb {R}\) .
Therefore, the elements of \(\mathbf {y}\)  and \(\mathbf {K}\)  must be encoded into plaintext before encryption [1]}, [2]}, [3]}.
This encoding process is omitted in this study because it is focused on the cryptographic properties of the encrypted controls.

